Rewrite as a simplified fraction. ${0.1\overline{52} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 152.5252...\\ 10x &= 1.5252...\end{align*}}$ Subtracting the two equations, we have: ${990x = 151}$ ${x = \dfrac{151}{990}} $